In a small bowl, combine Bisquick mix, egg, and milk. Whisk until combined. Season with salt and pepper. Fold in Swiss cheese and ham.
In an electric skillet, heat 1-1/2 in. of oil to 375°. Drop batter by rounded tablespoonfuls, a few at a time, into hot oil. Fry until golden brown, about 1 minute on each side. Drain on paper towels. Garnish with sliced green onions, if desired. Serve warm with warm cheese sauce, if desired.